Cooperative co-evolution (CC) algorithms, based on the divide-and-conquer strategy, have emerged as the predominant approach to solving large-scale global optimization (LSGO) problems. The efficiency and accuracy of the grouping stage significantly impact the performance of the optimization process. While the general separability grouping (GSG) method has overcome the limitation of previous differential grouping (DG) methods by enabling the decomposition of non-additively separable functions, it suffers from high computational complexity. To address this challenge, this article proposes a composite separability grouping (CSG) method, seamlessly integrating DG and GSG into a problem decomposition framework to utilize the strengths of both approaches. CSG introduces a step-by-step decomposition framework that accurately decomposes various problem types using fewer computational resources. By sequentially identifying additively, multiplicatively and generally separable variables, CSG progressively groups non-separable variables by recursively considering the interactions between each non-separable variable and the formed non-separable groups. Furthermore, to enhance the efficiency and accuracy of CSG, we introduce two innovative methods: a multiplicatively separable variable detection method and a non-separable variable grouping method. These two methods are designed to effectively detect multiplicatively separable variables and efficiently group non-separable variables, respectively. Extensive experimental results demonstrate that CSG achieves more accurate variable grouping with lower computational complexity compared to GSG and state-of-the-art DG series designs.

翻译：基于分治策略的协同进化算法已成为解决大规模全局优化问题的主流方法。分组阶段的效率与精度对优化过程的性能具有决定性影响。通用可分离性分组方法通过实现非加性可分离函数的分解，克服了此前差分分组方法的局限性，但其计算复杂度较高。针对这一挑战，本文提出了一种复合可分离性分组方法，将差分分组与通用可分离性分组无缝融合到问题分解框架中，从而整合两种方法的优势。该方法通过逐层分解框架，利用更少的计算资源精确分解各类问题。通过依次识别加性、乘性和通用可分离变量，复合可分离性分组方法通过递归考虑每个非可分离变量与已形成非可分离组之间的相互作用，逐步对非可分离变量进行分组。此外，为提升复合可分离性分组方法的效率与精度，我们引入了两种创新方法：乘性可分离变量检测方法与非可分离变量分组方法，分别用于高效检测乘性可分离变量和有效分组非可分离变量。大量实验结果表明，与通用可分离性分组方法及最先进的差分分组系列设计方案相比，复合可分离性分组方法能以更低计算复杂度实现更精确的变量分组。